We consider the generalized Choquard equation describing trapped electron gas in three dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p ≠ 2 is connected with possible lack of control on the Lp norm of the minimizers. Our main result treats the local uniqueness of radial positive minimizers for p ∈ (5∕3, 7∕3).